In this setting, we consider the vehicle lateral control problem from [1]}, [2]}. The goal is for the vehicle to track the lane edge while avoiding strong control inputs. The continuous-time linear vehicle lateral dynamics are
\(\scriptsize {\begin{bmatrix}\dot{e} \\ \ddot{e} \\ \dot{e}_\theta \\ \ddot{e}_\theta \end{bmatrix} = \begin{bmatrix}0 & 1 & 0&0 \\ 0 & \frac{C_{\alpha f} + C_{\alpha r}}{m U} & -\frac{C_{\alpha f} + C_{\alpha r}}{m} & \frac{a C_{\alpha f} - b C_{\alpha r}}{m U} \\ 0 & 0 & 0&1 \\ 0 & \frac{a C_{\alpha f} - b C_{\alpha r}}{I_z U} & -\frac{a C_{\alpha f} - b C_{\alpha r}}{I_z} & \frac{a^2 C_{\alpha f} + b^2 C_{\alpha r}}{I_z U}\end{bmatrix} \begin{bmatrix}e \\ \dot{e} \\ e_\theta \\ \dot{e}_\theta \end{bmatrix}+\begin{bmatrix}0 \\ -\frac{C_{\alpha f}}{m} \\ 0 \\ -\frac{a C_{\alpha f}}{I_z}\end{bmatrix} u + \begin{bmatrix}0\\ \frac{a C_{\alpha f} - b C_{\alpha r} - mU^2}{m} \\ 0 \\ \frac{a^2 C_{\alpha f} + b^2 C_{\alpha r}}{I_z}\end{bmatrix} c}\) 
